Banach Journal of Mathematical Analysis

p-maximal regularity for a class of fractional difference equations on UMD spaces: The case 1<α2

Carlos Lizama and Marina Murillo-Arcila

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Abstract

By using Blunck’s operator-valued Fourier multiplier theorem, we completely characterize the existence and uniqueness of solutions in Lebesgue sequence spaces for a discrete version of the Cauchy problem with fractional order 1<α2. This characterization is given solely in spectral terms on the data of the problem, whenever the underlying Banach space belongs to the UMD-class.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 1 (2017), 188-206.

Dates
Received: 12 October 2015
Accepted: 11 March 2016
First available in Project Euclid: 30 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1480474819

Digital Object Identifier
doi:10.1215/17358787-3784616

Mathematical Reviews number (MathSciNet)
MR3577375

Zentralblatt MATH identifier
1359.39003

Subjects
Primary: 47A10: Spectrum, resolvent
Secondary: 47A50: Equations and inequalities involving linear operators, with vector unknowns 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx] 35R11: Fractional partial differential equations 34A33: Lattice differential equations

Keywords
maximal regularity Lebesgue sequence spaces UMD Banach spaces R-boundedness lattice models

Citation

Lizama, Carlos; Murillo-Arcila, Marina. $\ell_{p}$ -maximal regularity for a class of fractional difference equations on UMD spaces: The case $1\lt \alpha\leq2$. Banach J. Math. Anal. 11 (2017), no. 1, 188--206. doi:10.1215/17358787-3784616. https://projecteuclid.org/euclid.bjma/1480474819


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